The invention relates to a receiver for a digital transmission system with an incoherent transmission method, which receiver includes an equalizer for forming estimates for a sequence of symbols a[k] transmitted by a transmission channel from received symbols r[k] by means of an impulse response h[k] that describes the transmission properties.
The invention further relates to an equalizer for a digital transmission system with an incoherent transmission method and to a mobile radiotelephone for a digital transmission system with an incoherent transmission method.
Such receivers are used in digital transmission systems, for example, in the digital mobile radiotelephone according to various international standards, which transmission systems comprise at least a transmitter, a transmission channel and a receiver. A data source in the transmitter (for example, a microphone with an A/D converter in a mobile radiotelephone) generates a sequence of binary symbols d[i]∈{0;1} which are subsequently modulated by means of an MDPSK (M-ary Differential Phase Shift Keying) modulation method. In a QPSK modulation (Quarternary Phase Shift Keying, with M=4), for example, two successive bits (00,01,10,11) in a mapper are shown on a QPSK symbol a[k]. These symbols are differentially coded in a precoder, so that symbols b[k]=a[k]xe2x80xa2b[kxe2x88x921] evolve. As a result, the symbols are not determined by the absolute phase position of the carrier frequency, but by the difference from the phase position of the previous symbol, which can be used in a receiver having an incoherent receiving method. The determination of an absolute phase position leads to problems during the demodulation, which problems are caused by phase ambiguities. With a quarternary DPSK modulation, there are relative phase differences between successive symbols b[k] of 0xc2x0, 90xc2x0, 180xc2x0 and xe2x88x9290xc2x0 (45xc2x0, 135xc2x0, xe2x88x92135 and xe2x88x9245xc2x0 respectively, with xcfx80/4 QDPSK) in dependence on the symbols 00,01,10 and 11. When a differential precoding of the symbols (QDPSK) is used, this is also known as an incoherent transmission method.
The sequence of symbols b[k] is transmitted by a possibly time-variant transmission channel which has distortion and noise. In a receiver input stage the received symbol r(t) is sampled with a symbol clock T, the sampling instant kT+t0 being determined by a synchronizer. The discrete sequence rxe2x80x2[k]=r(kT+t0 is obtained then. A subsequent standardization with the average efficiency of the received symbols rxe2x80x2[k] leads to the symbols r[k] which have the average efficiency 1. The symbols r[k] may be described with a desired symbol y[k] to which an interference portion n[k] is added. This noise sequence n[k] may be assumed to be white Gaussian noise.
By means of an equalizer, a receiver estimates the sequence of symbols xc3xa2[kxe2x88x92kmax] from the sampled values of the received signal, while this sequence must be a maximum match for the transmitted sequence a[k] except for the delay kmax. Estimates for the data sequence d[i] can be determined from the symbols xc3xa2[kxe2x88x92kmax] by means of a conversion of the mapping. The description of the formation of the transmission pulse, high-frequency modulation and transmission gain and, at the receiving end, the high-frequency demodulation and receiving filtering is omitted for clarity and only the baseband model is represented. The transmission properties of the whole transmission channel between the transmitter-end symbols b[k] and the received symbols r[k] are combined, in a time-invariant channel, to an overall impulse response h(t) or h[k] respectively, in the symbol clock model. In the case of a time-variant channel, that is to say, when the properties depend on time, the transmission properties of the channel are described by the channel impulse response h(xcfx84,t). In the following, this dependence on time will not be taken into account to clarify the representation. In the channel impulse response h(t) are included as transmission properties also the Inter-Symbol Interference (ISI) of the linearly distorting transmission channel, which ISI is caused by multipath propagation of the signal. The mixing of the baseband signal with a high-frequency carrier signal in non-synchronized Local Oscillators (LO) leads to a phase and frequency offset which produces additional intersymbol interference upon reception.
In an incoherent receiver, the absolute phase position of a received symbol is not determined within the symbol interval. Only the relative phase difference of successive symbols is determined. This is habitually achieved by differentiating the sampling frequency of the received signals by means of a multiplication by the conjugate-complex symbol sampling frequency shifted by one symbol interval. The absolute phase position of the carrier frequency is then eliminated from the sequence of desired signals. Also Rayleigh fading occurring in mobile radiotelephone systems causes a frequency offset of the received signal to occur, as a result of which an incoherent receiving method is advantageous.
When receivers with incoherent receiving methods have transmission channels in which a symbol received in interval k is also influenced by Lxe2x88x921 previous symbols, they have high bit error rates when the received symbols are detected. L denotes the number of symbols superimposed in the interval k as a result of multipath propagation, for example, which may be described with a memory length Lxe2x88x921 of the transmission channel (having a discrete channel impulse response of h=[h(0),h(1), . . . h(Lxe2x88x921)]) and leads to intersymbol interference (ISI). The superpositioning leads to a sequence of desired symbols y[k] which are described by the sum       y    ⁡          [      k      ]        =            ∑              l        =        0                    L        -        1              ⁢                  h        ⁡                  [          l          ]                    ·              b        ⁡                  [                      k            -            l                    ]                    
In xe2x80x9cDigital Communicationsxe2x80x9d, 3rd Edition, MgGraw-Hill International Editions, 1995, by John G. Proakis, is described a receiving method for differential. PSK (DPSK) with channels that have no pulse interference. From page 274 onwards is shown the reception of differentially coded, phase-modulated signals. As appears from the processing shown of the received symbol r(t), the phase position of the carrier signal need not be estimated. With the multiplication of the sample value r[k] of a received signal r(t) by the conjugate-complex value of the previous value r*[kxe2x88x921], the phase position of the carrier signal disappears from the defining equation, so that only the difference between the phase angle of the signal at instant k and the phase angle of the previous signal (kxe2x88x921) needs to be detected. Consequently, this MDPSK method is also referred to as an incoherent receiving method. Since the channel memory is discarded for this method, the bit error rate of channels having intersymbol interference is very high.
From the article xe2x80x9cNonlinear Equalization of Multipath Fading Channels with Noncoherent Demodulationxe2x80x9d, Ali Masoomzadeh and Subarayan Pasupathy, IEEE Journal on Selected Areas in Communications, vol. 14, no. 3, April 1996, pp. 512-520 is known an equalizer for MDPSK-modulated signals. For these MDPSK signals is then proposed a receiving method with a distorting transmission channel and non-linear intersymbol interference (ISI), which interference arises from the differentiation in the receiver. In the incoherent receiver a decision feedback equalization DFE is used for the detection. Owing to the non-linear distortions as a result of the differentiation, the conventional DFE cannot be used. Therefore, it is necessary to implement a modified DFE method which also takes the non-linear distortion into account in the xe2x80x9cDigital Communicationsxe2x80x9d mentioned above, non-linear DFE equalization for an MDPSK signal, for which equalization the equalizer in the receiver follows the differential decoder. This equalizer may equalize the non-linear ISI produced by the differential decoder. Such an incoherent receiving method clearly provides poorer results in transmission channels without frequency and phase offset than a coherent method. There may be detected a loss of more than 8 dB in the power efficiency compared with an optimum coherent MLSE receiver.
Therefore, it is an object of the invention to improve the receiving quality, that is, the correspondence of the estimated symbols with the transmitted symbols in an incoherent transmission method and in transmission channels having intersymbol interference.
The object is achieved in that for determining the estimates xc3xa2[k] for the sequence of transmitted symbols a[k] the equalizer performs an incoherent maximum-likelihood sequence estimation (MLSE) method. According to the MLSE method, the estimates xc3xa2[k] are determined by means of a defined probability density function relating to a sequence of received symbols r[k] with a presupposed, undisturbed sequence of desired symbols y[k], while the absolute phase of the desired symbol sequence y[k] or the incoherence need not be taken into account. The undisturbed sequence of desired symbols y[k] is formed by means of the channel impulse response h[k] assumed to be known, except for the absolute phase, for each possible sequence of transmitted symbols a[k] formed by N+1 symbols. For determining the transmitted sequence of symbols a[k], the probability of correspondence of the sequence of symbols y[k] with the received sequence of symbols r[k] is maximized by means of the probability density function, while the absolute phase of y[k] with the incoherent MLSE method has no effect on the maximization. This maximization leads to a minimum error probability sequence which then forms the sequence of estimates xc3xa2[k] for the sequence of transmitted symbols a[k]. This means that the correspondence of the sequence xc3xa2[k] with the sequence a[k], which is optimum with the incoherent transmission method, is achieved. As a strictly monotonous exponential function is used for the probability density function, a simpler minimization of a metric xcex can be carried out instead of the maximization. The optimum, incoherent metric xcex makes the best estimate of the sequence of transmitted symbols a[k] possible. The equalizer may comprise, for example, a digital signal processor or another processor to which the received symbols r[k] and the overall impulse response h[k] can be applied and which carries out the necessary computations for determining the estimates xc3xa2[k] for the transmitted symbols a[k].
In an advantageous embodiment of the receiver, the equalizer divides the received symbols r[k] into at least two symbol blocks having at least two symbols each, forms symbol blocks overlapping by at least one symbol r[k] and forms the estimates xc3xa2[k] for the transmitted symbols a[k] symbol block by symbol block. Since the optimum metric xcex does not have a recursive structure, the evaluation of this metric xcex is very costly. A cost-effective realization is made possible by the formation of symbol blocks. For this purpose, the equalizer writes the received symbols r[k], for example, into a buffer memory and forms the symbol blocks in that it consecutively reads a definable number of symbols (a symbol block) and applies them to the estimation method. For example, a digital memory may then be provided as a buffer, while the digital signal processor takes over control. Preferably, memory and processor are integrated into one IC. As a result of the buffering the sequence of the received symbols r[k] is thus subdivided into Ng symbol blocks having a length of NB greater than 1 symbols each. For determining estimates, N+Lxe2x88x921 symbols are to be considered, so that Ng(NBxe2x88x921)=N+Lxe2x88x921 holds. Consecutive symbol blocks overlap by at least one symbol, that is to say, the last symbols of a symbol block are repeated at the beginning of the next symbol block. This is necessary for rendering one reference phase for each symbol block available for the incoherent receiving method used. The subdivision into symbol blocks causes a sub-optimum metric (block metric) to evolve from the optimum metric, while the minimization of the sub-optimum metric corresponds to an estimate in symbol blocks. The block metric has a recursive structure, so that a cost-effective realization becomes possible. The reliability of the estimates xc3xa2[k] and the cost of implementation are enhanced when the symbol block length increases, so that a compromise between power efficiency and cost can be reached.
In a preferred embodiment of the invention, the equalizer carries out the estimation in symbol blocks of the sequence of transmitted symbols a[k] by means of a Viterbi algorithm. The block metric realized by means of the known Viterbi algorithm makes a cost-effective implementation possible as the advantages of the recursive structure are used. Each symbol block of the sequence of received symbols r[k] then corresponds to a step in time in a trellis diagram allocated to the Viterbi algorithm.
Further preferred embodiments are defined in the remaining dependent claims. More particularly, simulations have shown that a subdivision of the sequence of received symbols r[k] by the equalizer into symbol blocks of 3 or 2 symbols is advantageous. Furthermore, the receiver according to the invention is arranged highly effectively when the equalizer forms symbol blocks which overlap by exactly one symbol r[k].
The object of the invention is also achieved by the equalizer and the mobile radiotelephone having the features according to the invention.
These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter.